Preheat the oven to 350°F.
In a medium saucepan, combine the brown sugar, boiling water, and butter.
Place the saucepan over medium-high heat and bring the mixture to a boil.
Allow the sauce to boil for 2 minutes, stirring occasionally until the brown sugar is dissolved and the butter is fully melted.
Carefully pour the hot sauce into a 9-inch square baking dish.
In a large mixing bowl, combine the all-purpose flour, granulated sugar, milk, raisins, baking powder, egg, and salt.
Stir the ingredients together until a thick batter forms and all dry ingredients are incorporated.
Do not overmix the batter, as this may affect the final texture of the pudding.
Using a large tablespoon, drop spoonfuls of the batter evenly into the hot brown sugar sauce.
Space the batter portions across the baking dish to help the pudding bake evenly.
Place the baking dish in the preheated oven.
Bake for approximately 30 minutes, or until the top is golden brown and the pudding portion is set.
Remove the baking dish from the oven.
Allow the pudding to cool for 5 to 10 minutes before serving.
Serve warm, spooning each portion with some of the brown sugar sauce from the bottom of the dish.